CHI-SQUARE TESTS: Statistical Analysis of Drosophila Generations

Transcription

1 CHI-SQUARE TESTS: Statistical Analysis of Drosophila Generations Lab #7 Heredity & Human Affairs

2 CHI-SQUARE TEST X 2 Test a.k.a. The Goodness-of-Fit test Statistical test used for analyzing results of an experiment. How do your actual results compare with your predictions? In other words, how good do your results fit with your predicted results.

3 CHI-SQUARE TEST Today: Let s test how your F 2 Drosophila counts (from last week) compare with the predictions you made using Punnett Squares.

4 Recall Punnett Square Autosomal Mutation: Apterous F 1 : (+, ap) For your counts, did you get exactly 3 winged for every 1 apterous fly? Probably not. (+, ap) Wing mutation + ap ap 3 winged : F 2 s 1 apterous ap + ap ap ap (predicted phenotypic ratio)

5 Recall Punnett Square Sex-Linked Mutation: White-Eyes F 1 : (X W Y) (X + X w ) For your counts, did you get exactly 1:1:1:1 ratio? Probably not. Eye-color mutation X w Y 1 red-eyed female: 1 X white-eyed + X + X w female: X + Y 1 red-eyed male: F 2 s 1 white-eyed X w X w X w male X w Y (predicted phenotypic ratio)

6 Does it matter? Are your counts close enough to the predicted numbers? If yes, then with what level of confidence? If no, what could be the cause of this deviation?

7 CHI-SQUARE TEST The Formula: O = observed data E = expected data X 2 = (O E) 2 E

8 CHI-SQUARE TEST Why do a chi-square test? Commonly used to compare observed data with data we would expect to obtain according to a specific hypothesis. Compares OBSERVED values to determine if these are close enough to EXPECTED (E) values (hypothesis) to be considered valid. Are deviations from expected values due to chance alone or some other factor?

9 CHI-SQUARE TEST Observing PROBABILITY, not possibility Example: coin flip»probabilities: heads or tails (2)»Possibilities: heads, tails, side, never come down, etc. (4 + )

10 CHI-SQUARE TEST Scientists use a high confidence level (or probability) to check the hypothesis in question. Scientists use a Probability > 95% This means that any differences observed are likely due to chance alone. Only a 5% chance that something else is responsible for the variation. Likewise, 95% chance that it s a random variation due to chance!

11 Degrees of Freedom = n 1 n= number of classes or categories

12 Fun Fact of the Day: Chi Square Created by Karl Pearson 1857 to 1936 in England Originally named Carl Changed at 23 Had 3 kids- Egon Sigrid Helga Professor of Applied Mathematics and Zoology

13 Fun Fact of the Day: Chi Square Published 18 papers from 1893 to 1912 Mathematical Contributions to the Theory of Evolution 1900: Chi-square test of statistical significance Had a long, very soap opera- ish battle with fellow statistician Sir Ronald Fisher Fisher added the Degrees of Freedom

14 Coin Toss Example When you flip a coin, what are the possibilities? What are the two probabilities?» It will land on heads. It will land on tails. Will the penny land on heads exactly 50% of the time? Tails exactly 50% of the time? If not, is the deviation from the expected results due to chance alone or some other reason? What could be the reason it does not land on heads exactly 50% of the time?

15 How to apply the X 2 Test Class Coin Toss Example: (page 57) # of heads / class total = # of tails / class total = TOTAL: How do you figure out the expected values? Total the number of coin tosses. Then, divide by 2 since it s a 1:1 (50:50) expected ratio of heads : tails. Classes O E O E (O E) 2 (O E) 2 E Heads Tails

16 1) What is the X 2 value & where does it fit on this chart? 2) What is the probability? 3) Do you: ACCEPT / No Reason to Doubt Hypothesis or REJECT / Reason to Doubt Hypothesis

17 Now your fly data!

18 Observed Results for SPRING 2012 Page 58 Exercise #2: SEX RATIOS Males = Females = TOTAL:

19 Observed Results for SPRING 2012 Page 59 Exercise #3: AUTOSOMAL MUTATION WILD vs. APTEROUS Wild ( normal wings ) = 2523 Apterous = How do you figure out the expected TOTAL: values? Expected ratio is 3:1 (3 winged : 1apterous), so expected numbers = total flies counted divided by 4 or times 75% & times 25%.

20 Observed Results for SPRING 2012 Page 60 Exercise #4: SEX-LINKED MUTATION WHITE-EYED vs. RED-EYED 771 Males, White Eyes = Females, White Eyes = Males, Red Eyes = How do you figure Females, Red Eyes = out the expected 3345 values? TOTAL: Expected ratio is 1:1:1:1, so expected numbers = total flies counted divided by 4 or 25%.

21 OMIT! Page 61, Chi-Square Practice Dihybrid Corn

22 TODAY: Work through the X 2 problems in the lab packet. Try to do so ON YOUR OWN! These pages will be counted as your post-lab grade. Ask instructor for help, if you need it. You will need to know how to do these problems on your own for the Final Lab Practical Exam! Hand in completed problems before the end of lab today. SHOW ALL WORK! Nothing additional will be due. No Lab Next Week. Enjoy your Spring Break